f

Stat/TP3/Exercice2_Caesar/c.py

+
+import math
 import string
-from turtle import width
 import pandas as pd
 import matplotlib.pyplot as plt
 import numpy as np
@@ -31,14 +32,6 @@ def caesar_crypt(msg,decal):
                     msg_crypt+=new_alphabet[y]
     return msg_crypt
 
-def txtcryptjson(fichier,decal):
-    with open(fichier,"r",encoding="UTF-8") as txt:
-        new_file = open("crypted_with_caesar.txt","w")
-        str=txt.read()
-        strcry=caesar_crypt(str, decal)
-        new_file.write(strcry)
-        new_file.close()
-        filetofreq("crypted_with_caesar.txt","freq2.json")
 
 def filetofreq(text,fichier):
     new_file = open(fichier,"w")
@@ -59,7 +52,6 @@ def bar_freq(fichier):
     yAxis = [value for key, value in dictionary.items()]
 
     fig, ax = plt.subplots()
-    plt.xticks(rotation=35,ha="right")
     ax.bar(xAxis,yAxis)
     plt.tight_layout()
     ax.set_title("Fréquence d'apparition d'une lettre")
@@ -75,24 +67,99 @@ def bar_freq1_freq2(fichier1,fichier2):
     yAxis2 = [value for key, value in dictionary2.items()]
 
     fig, ax = plt.subplots()
-    plt.xticks(rotation=35,ha="right")
-    ax.bar(np.arange(len(xAxis))+0.2,yAxis,0.4)
-    ax.bar(np.arange(len(xAxis2))-0.2,yAxis2,0.4)
+    ax.bar(np.arange(len(xAxis))+0.2,yAxis,0.4,label="Freq 1")
+    ax.bar(np.arange(len(xAxis2))-0.2,yAxis2,0.4,label="Freq 2")
     plt.tight_layout()
+    plt.legend()
     ax.set_title("Fréquence d'apparition d'une lettre")
     plt.show()
 
 def bar_compare_freq(fichier1,fichier2,decal):
-    txtcryptjson(fichier2,decal)
-    bar_freq1_freq2(fichier1,fichier2)
+    dictionary = json.load(open(fichier1, 'r'))
+    xAxis = [key for key, value in dictionary.items()]
+    yAxis = [value for key, value in dictionary.items()]
+    dictionary2 = json.load(open(fichier2, 'r'))
+    xAxis2 = [key for key,value in dictionary2.items()]
+    yAxis2 = [value for key, value in dictionary2.items()]
+    yAxis2=yAxis2[decal:]+yAxis2[:decal]
+
+    fig, ax = plt.subplots()
+    ax.bar(np.arange(len(xAxis))+0.2,yAxis,0.4,label="Freq 1")
+    ax.bar(np.arange(len(xAxis2))-0.2,yAxis2,0.4,label="Freq 2")
+    plt.tight_layout()
+    plt.legend()
+    ax.set_title("Fréquence d'apparition d'une lettre")
+    plt.show()
+
+def manualdecrypt(fichier1,fichier2):
+    for i in range(1,26):
+        print("décalage :",i) 
+        bar_compare_freq(fichier1,fichier2,i)
+
+
+def moy(x):
+    add=0
+    for e in x:
+        add+=e
+    return add/len(x)
+
+def covar(X,Y):
+    som=0
+    if len(X) == len(Y):
+        for i in range(0,len(X)):
+            a=(X[i]-moy(X)) * (Y[i]-moy(Y))
+            a/=len(X)
+            som+=a
+            a=0
+        return som
+    else:
+        return "error"
+
+def variance(X):
+    a=0
+    for i in range(0,len(X)):
+        a+=(X[i]-moy(X))**2
+    return a*(1/len(X))
+
+def coeff_corr(X,Y):
+    return covar(X,Y)/(math.sqrt(variance(X)*variance(Y)))
+
+def correlation_freqs(fichier1,fichier2):
+    dictionary = json.load(open(fichier1, 'r'))
+    yAxis = [value for key, value in dictionary.items()]
+    dictionary2 = json.load(open(fichier2, 'r'))
+    yAxis2 = [value for key, value in dictionary2.items()]
+
+    corr=-1
+    decal=0
+
+    for i in range(1,26):
+        yAxis2=yAxis2[1:]+yAxis2[:1]
+        print("décalage :",i," crypt correlation :",coeff_corr(yAxis,yAxis2))
+        if corr<coeff_corr(yAxis,yAxis2):
+            decal=i
+            corr=coeff_corr(yAxis,yAxis2)
+    print("Décalage de décryptage :", decal)
+    return decal
+
+def decrpt(fichier):
+    filetofreq(fichier,"freq.json")
+    with open(fichier,"r",encoding="UTF-8") as txt:
+        new_file = open("decrypted_with_caesar.txt","w")
+        str=txt.read()
+        strdecry=caesar_crypt(str,-correlation_freqs("freq_lettre_fr.json","freq.json"))
+        new_file.write(strdecry)
+        new_file.close()
 
 def main():
     filetofreq("encrypted_with_caesar.txt","freq1.json")
-    txtcryptjson("encrypted_with_caesar.txt",3)
     
-    #bar_freq("freq1.json")
-    #bar_freq1_freq2("freq1.json","freq2.json")
-    bar_compare_freq("freq1.json","freq2.json",0)
+    #bar_freq("freq_lettre_fr.json")
+    #bar_freq1_freq2("freq_lettre_fr.json","freq1.json")
+    #bar_compare_freq("freq_lettre_fr.json","freq1.json",3)
+    #manualdecrypt("freq_lettre_fr.json","freq1.json") #ici c'est 17 de décalage
+    correlation_freqs("freq_lettre_fr.json","freq1.json")
+    decrpt("encrypted_with_caesar.txt")
         
 
 main()
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Stat/TP3/Exercice2_Caesar/crypted_with_caesar.txt

-abcdefghijklmnopqrstuvwxyz
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Stat/TP3/Exercice2_Caesar/decrypted_with_caesar.txt

+LECHIFFREMENTPARSUBSTITUTIONESTUNETECHNIQUEDECHIFFREMENTUTILISEEDEPUISBIENLONGTEMPSPUISQUELECHIFFREDECESARENESTUNCASPARTICULIERSANSAUTREPRECISIONELLEDESIGNEENGENERALUNCHIFFREMENTMONOALPHABETIQUEQUICONSISTEAECHANGERDANSUNMESSAGECHACUNDESCARACTERESDELALPHABETPARUNAUTREQUANDLALPHABETDARRIVEEESTLEMEMELASUBSTITUTIONESTDEFINIEPARUNEPERMUTATIONDESCARACTERESDELALPHABETCECHIFFREMENTESTASSEZSIMPLEACASSERPARANALYSEDESFREQUENCESDESSIGNESDUTEXTECHIFFREMAISILRESTEENCOREUTILISECOMMEPARTIEDESCERTAINSCHIFFREMENTSACTUELSAFINDEBROUILLERLANALYSEPARFREQUENCESDIVERSESTECHNIQUESDESUBSTITUTIONPLUSOUMOINSELABOREESONTETEINVENTEESAUCOURSDESSIECLESCOMMELESCHIFFREMENTSPARSUBSTITUTIONHOMOPHONIQUEOUPARSUBSTITUTIONPOLYALPHABETIQUELASUBSTITUTIONMONOALPHABETIQUEESTUNEDESPLUSANCIENNESMETHODESDECHIFFREMENTELLECONSISTEAREMPLACERDANSLEMESSAGECLAIRUNCARACTEREDONNEDELALPHABETPARUNSIGNEDONNEDEUXCARACTERESDISTINCTESDOIVENTETRECHIFFREESENDEUXSIGNESDISTINCTSAUQUELCASILYAURAITAMBIGUITELORSDUDECHIFFREMENTUNMEMECARACTEREESTTOUJOURSCHIFFREPARLEMEMESIGNECESTLEPRINCIPEDELASUBSTITUTIONMONOALPHABETIQUELASUBSTITUTIONPOLYALPHABETIQUESEFAITENSUBSTITUANTUNSIGNEDUMESSAGEENCLAIRPARUNEAUTRECHOISIEENFONCTIONDUNETATDUCRYPTOSYSTEMEETNONPLUSDEMANIEREFIXECOMMEPOURLAMONOSUBSTITUTIONCECHANGEMENTDELETTRETOUTAULONGDUPROCEDESOBTIENTALAIDEDUNECLEQUIINDIQUELENOMBREDEDECALAGEAREALISERACEMOMENTPOURCHIFFRERLESIGNESUIVANTONUTILISEALORSLECARACTERESUIVANTDELACLEETAINSIDESUITEONRECOMMENCEAUDEBUTDELACLEQUANDTOUSSESSIGNESSONTUTILISESLAPLUSCELEBREUTILISATIONDECETTETECHNIQUERESTELAMACHINEALLEMANDEENIGMADELADEUXIEMEGUERREMONDIALE
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Stat/TP3/Exercice2_Caesar/freq.json

+{"a": 0.06353240152477764, "b": 0.0, "c": 5.082592121982211, "d": 3.1130876747141043, "e": 7.306226175349428, "f": 4.193138500635324, "g": 2.6048284625158833, "h": 1.1435832274459974, "i": 5.336721728081321, "j": 8.259212198221093, "k": 7.814485387547649, "l": 6.289707750952986, "m": 0.3811944091486658, "n": 0.0, "o": 0.3176620076238882, "p": 0.44472681067344344, "q": 0.06353240152477764, "r": 7.496823379923762, "s": 1.7153748411689964, "t": 4.701397712833545, "u": 3.6213468869123253, "v": 16.96315120711563, "w": 2.096569250317662, "x": 1.2706480304955527, "y": 2.096569250317662, "z": 7.6238881829733165}
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Stat/TP3/Exercice2_Caesar/freq2.json

-{"a": 3.8461538461538463, "b": 3.8461538461538463, "c": 3.8461538461538463, "d": 3.8461538461538463, "e": 3.8461538461538463, "f": 3.8461538461538463, "g": 3.8461538461538463, "h": 3.8461538461538463, "i": 3.8461538461538463, "j": 3.8461538461538463, "k": 3.8461538461538463, "l": 3.8461538461538463, "m": 3.8461538461538463, "n": 3.8461538461538463, "o": 3.8461538461538463, "p": 3.8461538461538463, "q": 3.8461538461538463, "r": 3.8461538461538463, "s": 3.8461538461538463, "t": 3.8461538461538463, "u": 3.8461538461538463, "v": 3.8461538461538463, "w": 3.8461538461538463, "x": 3.8461538461538463, "y": 3.8461538461538463, "z": 3.8461538461538463}
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